Hi!Question:The helicopter view in the fiure below shows two people pulling on a stubborn mule. Asume that F1 is 110N, and F2 si 70N. The forces are measured in units of newtons(N).
a.Find the single force that is equivalent to the two forces shown.
magnitude____N
direction____degree(counterclockwise fromt the +-axis.
b.Find the force that a third person would have to exert on the mule to make the net force equal to zero.
magnitude___N
direction____degree(counterclockwise fromt the +-axis.Thank you
To find the single force that is equivalent to the two forces shown (F1 and F2), you need to use vector addition. The magnitude of the single equivalent force can be found by taking the sum of the magnitudes of F1 and F2:
Magnitude = F1 + F2
= 110N + 70N
= 180N
To find the direction of the single equivalent force, you can use trigonometry. Determine the angle of each individual force with respect to the x-axis, and then use the angle addition formula to find the resultant angle.
For F1:
Given that F1 is 110N, you also need to know its angle with respect to the x-axis. Let's assume it is θ1 degrees.
For F2:
Given that F2 is 70N, you also need to know its angle with respect to the x-axis. Let's assume it is θ2 degrees.
Using the magnitude and angles, you can use trigonometry to find the x and y components of each force:
F1x = F1 * cos(θ1)
F1y = F1 * sin(θ1)
F2x = F2 * cos(θ2)
F2y = F2 * sin(θ2)
Now, add the x and y components together:
Fx = F1x + F2x
Fy = F1y + F2y
Finally, find the magnitude and direction of the single equivalent force:
Magnitude = sqrt(Fx^2 + Fy^2)
Direction = atan(Fy / Fx) + 180° (to account for the counterclockwise direction)
To find the force that a third person would have to exert on the mule to make the net force equal to zero, you need to create an equation using vector addition.
Let's assume this third force is F3 with magnitude F3 and an angle with respect to the x-axis of θ3 degrees.
Using trigonometry, you can calculate the x and y components of F3:
F3x = F3 * cos(θ3)
F3y = F3 * sin(θ3)
Now, create an equation by summing up the x and y components of all three forces and setting them equal to zero:
F1x + F2x + F3x = 0
F1y + F2y + F3y = 0
Substituting the values from F1, F2, F1x, F1y, F2x, and F2y, you can solve for F3 and determine its magnitude and direction.
Magnitude = sqrt(F3x^2 + F3y^2)
Direction = atan(F3y / F3x) + 180° (to account for the counterclockwise direction)
a. To find the single force equivalent to the two forces, we need to find the vector sum of F1 and F2.
Using vector addition, we can find the resultant force by adding the magnitudes of F1 and F2 using the Pythagorean theorem. The direction of the resultant force can be found using inverse tangent or trigonometric identities.
Magnitude of the resultant force:
Resultant force = √(F1^2 + F2^2)
Resultant force = √(110^2 + 70^2)
Resultant force = √(12100 + 4900)
Resultant force = √17000
Resultant force ≈ 130.38 N
Direction of the resultant force:
Inverse tangent can be used to find the angle/counterclockwise direction.
Direction = tan^(-1)(F2/F1)
Direction = tan^(-1)(70/110)
Direction ≈ 32.66 degrees
Therefore, the magnitude of the resultant force is approximately 130.38 N, and the direction is approximately 32.66 degrees counterclockwise from the + axis.
b. To make the net force equal to zero, the third person needs to exert a force equal in magnitude and opposite in direction to the resultant force.
Magnitude of the force required:
Magnitude of the force required = Magnitude of the resultant force = 130.38 N
Direction of the force required:
Since the net force needs to be zero, the direction of the force required will be opposite to the direction of the resultant force.
Direction = Direction of the resultant force + 180 degrees
Direction ≈ 32.66 degrees + 180 degrees
Direction ≈ 212.66 degrees
Therefore, the magnitude of the force required is approximately 130.38 N, and the direction is approximately 212.66 degrees counterclockwise from the + axis.